Filippo Inzaghi needs a new song. "Oi oi oi, Pippo Inzaghi segna per noi," intoned Milan's supporters as they celebrated his appointment as manager this July. More than 2,000 of them had come to see his unveiling at Casa Milan, the club's glitzy new headquarters in the north-west of the city. They were asking him to "score us a goal", just for old time's sake.

They were destined to be disappointed. Two years on from his last match Inzaghi has no plans to come out of retirement. But you could hardly blame the fans for indulging in a little nostalgia. There has not been much to celebrate in their club's recent history.

Milan finished eighth in Serie A last season, their lowest position in more than 15 years. Everything that could go wrong did. Mario Balotelli missed a penalty for the first time in his career before sulking his way through the rest of the campaign. Boardroom power struggles destabilised the club. Stephan El Shaarawy lost almost the entire year to injury.

In January Milan took a chance on a rookie manager – sacking Massimiliano Allegri and replacing him with Inzaghi's former team-mate, Clarence Seedorf. On paper the Dutchman did well inheriting a team that had won just five of its first 19 league games and guiding it to 11 victories over the remaining 19. But but Seedorf was still fired at the end of the campaign after his methods were criticised by members of Milan's backroom staff. The club's long-time assistant manager, Mauro Tassotti, suggested that he would have quit if the manager had been retained.

He was also popular with the fans. They appreciated Inzaghi's goals but above all his reputation as an overachiever, a player who had overcome the deficiencies in his technique and physique through sheer bloody-mindedness and hard work, a man who, in the words of Johan Cruyff, "can't actually play football at all" but nevertheless scored 70 goals in European club competition over the course of his career.

For Inzaghi succeeding at football was always a case of mind over matter. He will take the same approach into management. Italian coaches who study for their Uefa licence at the national training centre in Coverciano are required to submit a master's thesis on a subject of their choice. Inzaghi's was titled "A Mentality For 'Being' A Winner".

He covers a range of topics over the document's 60 pages, from the importance of fair play through to the challenges of working together as a group. Inzaghi advises coaches to turn everything into a competition, setting players against one another in training and creating friendly wagers between them.

At youth level, at least, his approach has seemed to work. After hanging up his boots in 2012 immediately took charge of Milan's Under-17 team, leading them to victory over Zenit St Petersburg in the final of the Scopigno Cup. Promoted to look after the Under-21 side, he then won Italy's prestigious Viareggio Tournament, which Milan had not conquered since 2001.

Early results with the senior team have not been quite so encouraging. It is always dangerous to read too much into friendlies but Milan's performances during the Guinness Cup – a US-based pre-season tournament – bordered on the disastrous. The Rossoneri conceded 10 goals and scored only once in consecutive defeats by Olympiakos, Manchester City and Liverpool.

Inzaghi chose to look on the bright side, telling reporters that he had seen improvement in his team's final game. He has never been a man to dwell too long on the negatives. As he writes in the aforementioned thesis, "I always tell my players: I cried when I won, never when I lost."

It was also true that Milan could afford to be a little further behind in their preparations. The Serie A season does not begin until 31 August. There is time yet for the Rossoneri to address weaknesses in central midfield and across the back, although fans probably ought not to hold their breath. Milan's most notable additions so far this summer have been Alex and Jérémy Ménez, both acquired on free transfers from Paris Saint-Germain. For the team to spend any significant sum will require sales first. Getting Robinho off the books would be a start., although the club hopes that Inzaghi will also be able to plug some gaps by bringing through players from his own successful youth teams.

The Rossoneri are not the only ones tightening their belts. Juventus and Roma have been this summer's biggest spenders in Serie A and yet their most expensive signings – Álvaro Morata and Juan Iturbe respectively – each cost less than £20m. Or, to put it another way, less than half of what Paris Saint-Germain paid to acquire David Luiz from Chelsea.

That is in part a reflection of the new world order, one in which Serie A has declined and harsh economic realities are finally forcing clubs to live within their means. But it is also an indication of the fact that none of Italy's biggest teams have been forced to sell a star player so far this summer, transactions which tend to bring fresh money into the market.

The league's only high-profile departure has been the Juventus manager, Antonio Conte. That is a loss to the Old Lady and the league, yet many neutral fans will welcome it. After witnessing Juve smash the 100-point barrier en route to their third consecutive Scudetto, some of them had begun to feel nostalgic for a proper title race.